I've been learning Latin bit by bit using Orberg's Lingua Latina. At the end of chapter 6 there's the following sentence:

Verba Medi a Lydia laeta audiuntur

As far as I can understand it concerns Lydia hearing Medus' words and being happy. My confusion however is why Medus ends as Medi (which I think is genitive) but verba ends in 'a' and not verbis. A sentence prior to this one says this:

Lydia verbis Medi delactatur eumque salutat

Which I translated as 'Medus' words delight Lydia and she greets him'. Why is one sentence 'verbis' and the other 'verba'. Am I completely mis-translating it? Can someone shed some light on this?

Laetus,a,um is an adjective, so it will change in form to match the case/number/gender of the noun it goes with. In your first example, it matches with Lydia (and it's not just a coincidence that they're next to eachother). Lydia is ablative because it goes with the preposition "a," so "laeta" is also ablative. Thus, "The words of Medus are heard by a happy Lydia."

Don't rely on resemblence of endings alone. Verba ends with an A because it's a neuter plural (verbum, verbi, n.), and could thus be nom or acc plural. Lydia is feminine, so that long A has nothing in common. Ideally you'd have a macron over that A to help you tell them apart, but macrons are rare.

This should help you figure out the second example. "Lydia is pleased with the words of Medus and [she] greets him." Once you know that "words" here is ablative, you'll have to deduce the reason for this case. Here (as often) it's because the words are instrumental--you are delighted with or by something.